After having engine mounts replaced, the steering wheel was cocked sideways but the car tracks perfectly straight like that. The mechanic said it needs an alignment after their removal of the rack and pinion, so I had one and the car is perfectly to spec when the steering wheel is positioned straight - but driving like that still makes the car turn left unless the wheel is cocked about 15 degrees to the right.

The alignment guy did it twice and same results, he said it appears that the subframe is no longer perfectly centered between the wheels, causing the 4 wheels to be in a trapezoid shape. Is that possible and the most likely cause?

 

It is difficult to determine who knows the least about what they are doing, your mechanic or your alignment guy. If the vehicle tracks straight with the wheel off center then the mechanic did not center the rack when he changed the steering unit. If the alignment guy gets a good reading with the wheels straight his first clue would be the steering wheel is no longer centered.
I would not allow either one to remove and center the steering wheel.
I would go back to the mechanic have him center the wheels straight ahead and then ask why the steering wheel no longer aligns correctly. He needs to disconnect, center and reconnect the steering joint.

 

+1 Avern

Sorry if I'm being too technical. You can even show the tech this post.

Method 1: Most likely they went this route.
If they jacked or lifted the engine up to replace the engine mounts, there's no way the subframe can be sat in a crooked position because technically they didn't touch the subframe bolts. The tech didn't mark the steering coupler location on the rack prior to removing it. When they put the coupler back on the steering rack, they just eye balled it and called it a day. They need to figure out where the front wheels are perfectly straight, see where the steering wheel is at, drop the steering rack and reposition the coupler. Now that I think about it, they also need to see if they tightened all 3 steering rack bolts.

Method 2: Not likely they went this route.
If they supported the engine and dropped the subframe to access the engine mounts, they improperly repositioned the subframe going back. Also need to check either the subframe mounts to see if one came apart or if the bolts holding the mounts are loose.

Either way the car needs to go back and let them figure out where they made the mistake.

 

Thank you!